You are on an iceboat on frictionless, flat ice; you and theboat have a combined

Question

You are on an iceboat on frictionless, flat ice; you and theboat have a combined mass M. Along with you are two stones withmasses m1 and m2 such that M = 6.0000m1 =12.000m2. To get the boatmoving, you throw the stones rearward, either in succession ortogether, but in each case with a certain speed 12.000 m/srelative to the boat. What is the resulting speed of the boat ifyou throw the stones simultaneously?
What is the resulting speed of the boat if you throwthe stones m1 and then m2? What is the resulting speed of the boat if youthrow the stones m2 and then m1? You are on an iceboat on frictionless, flat ice; you and theboat have a combined mass M. Along with you are two stones withmasses m1 and m2 such that M = 6.0000m1 =12.000m2. To get the boatmoving, you throw the stones rearward, either in succession ortogether, but in each case with a certain speed 12.000 m/srelative to the boat. What is the resulting speed of the boat ifyou throw the stones simultaneously?
What is the resulting speed of the boat if you throwthe stones m1 and then m2? What is the resulting speed of the boat if youthrow the stones m2 and then m1?

Explanation / Answer

a) What is the resulting speed of the boat if youthrow the stones m1 and then m2?

Conservation of momentum (Keep in mind that the m2remains on board the boat)
(M + m2) vM -m1v1=0 then   vM= m1v1 /(M + m2 )
vM = m1 12 /(6.00m1 + 0.5m1)
vM = 12/ 6.5= 1.85 m/s
then we repeat for m2
(M+   m2 ) vM - M v'M    - m2v2 =0
vM' =[(m2v2 + (M+   m2 ) vM] / M
vM' = [(0.5m1 12+ (6m1+   0.5m1) 1.85] / 6m1

vM' = [(6 + (6.5 )1.85] / 6 = 3 m/s

vM'=3 m/s

What is the resulting speed of the boat if youthrow the stones m2 and then m1?

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